Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

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Spectral parameter

$R= 19.549801355$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.291858141
4 0.5
5 0.447213595
6 0.206374870
7 0.817698947
8 0.353553390
9 -0.914818825
10 0.316227766
11 0.437902289
12 0.145929070
13 -0.164021428
14 0.578200470
15 0.130522928
16 0.250000000
17 1.199969099
18 -0.646874594
19 -0.182150412
20 0.223606797
21 0.238652095
22 0.309643678
23 1.161258131
24 0.103187435
25 0.200000000
26 -0.115980664
27 -0.558855463
28 0.408849473
29 0.188202245
30 0.0922936480
31 -0.242085918
32 0.176776695
33 0.127805348
34 0.848506287
35 0.365686086
36 -0.457409412
37 -1.019450601
38 -0.128799791
39 -0.0478709893
40 0.158113883
41 1.065143286
42 0.168752514
43 0.705864727
44 0.218951144
45 -0.409119416
46 0.821133499
47 1.239396741
48 0.0729645353
49 -0.331368430
50 0.141421356
51 0.350220751
52 -0.0820107142
53 1.588328414
54 -0.395170487
55 0.195835857
56 0.289100235
57 -0.0531620808
58 0.133079083
59 -1.046179307
60 0.0652614643
61 -1.811725496
62 -0.171180594
63 -0.748046390
64 0.125000000
65 -0.0733526128
66 0.0903720284
67 -0.369676169
68 0.599984549
69 0.338922639
70 0.258579111
71 0.512904856
72 -0.323437297
73 1.082951367
74 -0.720860433
75 0.0583716282
76 -0.0910752062
77 0.358072241
78 -0.0338499011
79 -0.490406146
80 0.111803398
81 0.751712308
82 0.753170040
83 1.560692865
84 0.119326047
85 0.536642495
86 0.499121735
87 0.0549283575
88 0.154821839
89 1.860370704
90 -0.289291113
91 -0.134120149
92 0.580629065
93 -0.0706547463
94 0.876385840
95 -0.0814601408
96 0.0515937177
97 0.678840335
98 -0.234312864
99 -0.400601258
100 0.100000000
101 0.629194802
102 0.247643468
103 0.285598958
104 -0.0579903322
105 0.106728461
106 1.123117792
107 -0.933123467
108 -0.279427731
109 1.238844051
110 0.138476862
111 -0.297534958
112 0.204424736
113 0.751777552
114 -0.0375912678
115 0.519330424
116 0.0941011226
117 0.150049889
118 -0.739760482
119 0.981213485
120 0.0461468240
121 -0.808241560
122 -1.281083384
123 0.310870736
124 -0.121042959
125 0.0894427190
126 -0.528948675
127 1.487582971
128 0.0883883476
129 0.206012341
130 -0.0518681299
131 -0.840941763
132 0.0639026741
133 -0.148944100
134 -0.261400526
135 -0.249927761
136 0.424253143
137 0.970175003
138 0.239654496
139 -0.167946610
140 0.182843043
141 0.361728088
142 0.362678501
143 -0.0718260880
144 -0.228704706
145 0.0841666027
146 0.765762255
147 -0.0967164931
148 -0.509725300
149 -0.311400937
150 0.0412749741
151 -0.491801162
152 -0.0643998959
153 -1.097762080
154 0.253195309
155 -0.108264114
156 -0.0239354946
157 -1.356337087
158 -0.346769511
159 0.463518810
160 0.0790569415
161 0.949583783
162 0.531540870
163 -0.389652286
164 0.532571643
165 0.0571562893
166 1.103576508
167 0.771476555
168 0.0843762574
169 -0.973099299
170 0.379463547
171 0.167224920
172 0.352932363
173 -0.769178712
174 0.0388402140
175 0.163539789
176 0.109475572
177 -0.304316787
178 1.315480740
179 -1.233810297
180 -0.204559708
181 -1.298424591
182 -0.0948372672
183 -0.523326298
184 0.410566749
185 -0.455912169
186 -0.0499604502
187 0.530466454
188 0.619698370
189 -0.437352572
190 -0.0576010179
191 -1.555974381
192 0.0364822676